Deformation theory of dialgebra morphisms

Nijenhuis代数态射的算畴变形理论与极小模型

Deformations theory and minimal model of operads for Nijenhuis algebras morphisms

本文引入与Nijenhuis代数态射变形相关的新上同调理论，证明其上同调比较定理，并构造了控制该态射的算畴极小模型。

微分代数态射的上同调与形变

Cohomologies and deformations of differential algebra morphisms

该文研究微分代数态射的形式形变，构建对应上同调理论并证明上同调比较定理，最终给出权重为0的微分代数态射的极小模型。

Lie-Yamaguti 代数态射的形变上同调

Deformation cohomology of morphisms of Lie-Yamaguti algebras

本文研究 Lie-Yamaguti 代数态射的上同调，证明其控制形式形变，并揭示其与态射阿贝尔扩张的联系。

Morphisms Cohomology and Deformations of Hom-algebras

The purpose of this paper is to study deformation theory of Hom-associative algebra morphisms and Hom-Lie algebra morphisms. We introduce a suitable cohomology and discuss Infinitesimal deformations, equivalent deformations and obstructions. Moreover, we provide some examples.

Deformations of coalgebra morphisms

An algebraic deformation theory of coalgebra morphisms is constructed.

Deformation of dual Leibniz algebra morphisms

An algebraic deformation theory of morphisms of dual Leibniz algebras is obtained.

Cohomology and Deformations of $n$-Lie algebra morphisms

The study of $n$-Lie algebras which are natural generalization of Lie algebras is motivated by Nambu Mechanics and recent developments in String Theory and M-branes. The purpose of this paper is to define cohomology complexes and study deformation theory of $n$-Lie algebra morphisms. We discuss infinitesimal deformations, equivalent deformations and obstructions. Moreover, we provide various examples.

On Deformations of Associative Algebras

In a classic paper, Gerstenhaber showed that first order deformations of an associative k-algebra A are controlled by the second Hochschild cohomology group of A. More generally, any n-parameter first order deformation of A gives, due to commutativity of the cup-product on Hochschild cohomology, a morphism from the graded algebra Sym(k^n) to Ext^*(A,A), the Ext-algebra in the category of A-bimodules. We prove that any extension of the n-parameter first order deformation of A to an INFINITE ORDER formal deformation provides a canonical `lift' of the graded algebra morphism above to a dg-algebra…

Simultaneous deformations of algebras and morphisms via derived brackets

We present a method to construct explicitly L-infinity algebras governing simultaneous deformations of various kinds of algebraic structures and of their morphisms. It is an alternative to the heavy use of the operad machinery of the existing approaches. Our method relies on Voronov's derived bracket construction.

The L_\infty-deformation complex of diagrams of algebras

The deformation complex of an algebra over a colored PROP P is defined in terms of a minimal (or, more generally, cofibrant) model of P. It is shown that it carries the structure of an L_\infty-algebra which induces a graded Lie bracket on cohomology. As an example, the L_\infty-algebra structure on the deformation complex of an associative algebra morphism g, with the underlying cochain complex isomorphic to the Gerstenhaber-Schack complex of g, is constructed. Another example is the deformation complex of a Lie algebra morphism. The last example is the diagram describing two mutually inverse…